The Effect of Weak Cosmic Ray Heating Events on the Desorption of $\rm H_2$

Abstract: The typical amount of molecular hydrogen (${\rm H_2}$) in interstellar ices is not known, but significant freeze-out of ${\rm H_2}$ on dust grains is not expected. However, chemical models ubiquitously predict large amounts of $\rm H_2$ freeze-out in dense cloud conditions, and specialized treatments are needed to control the $\rm H_2$ population on grains. Here we present a numerical desorption model where the effect of weak heating events induced by cosmic rays (CRs) that heat grains to temperatures of a few tens of Kelvin at high frequencies is included, improving upon earlier desorption models that only consider strong heating events (maximum grain temperature close to 100 K) that occur at a low frequency. A temperature of a few tens of Kelvin is high enough to induce efficient desorption of $\rm H_2$, but we find that even the weak heating events do not occur often enough to lead to significant $\rm H_2$ desorption. Taking the weak heating events into account does affect the predicted abundances of other lightly-bound species, but the effect is restricted to low column densities. We make here the canonical assumption that the grains are spherical with a radius of 0.1 $\mu$m. It is conceivable that in the case of a grain size distribution, weak heating events could provide a boost to $\rm H_2$ desorption coming off small grains, which are the most numerous. Further studies are still required to better quantify the role of CRs in the desorption of $\rm H_2$ and other weakly bound species.